Two-dimensional RCFT's without Kac-Moody symmetry

TL;DR

This paper classifies a family of Rational Conformal Field Theories with two and three characters that lack Kac-Moody symmetry, revealing dualities with known models and connections to the Moonshine Module.

Contribution

It introduces a classification method for RCFTs without Kac-Moody symmetry using modular-invariant differential equations, identifying dual theories and their relations to the Moonshine Module.

Findings

Identified new RCFTs with two and three characters without Kac-Moody algebra.

Discovered dualities between these theories and minimal models, including the Moonshine Module.

Connected the dual of the Ising model to the Baby Monster Module.

Abstract

Using the method of modular-invariant differential equations, we classify a family of Rational Conformal Field Theories with two and three characters having no Kac-Moody algebra. In addition to unitary and non-unitary minimal models, we find "dual" theories whose characters obey bilinear relations with those of the minimal models to give the Moonshine Module. In some ways this relation is analogous to cosets of meromorphic CFT's. The theory dual in this sense to the Ising model has central charge 47/2 and is related to the Baby Monster Module.